Details

Introduction to Mechanical Vibrations


Introduction to Mechanical Vibrations


1. Aufl.

von: Ronald J. Anderson

63,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 06.03.2020
ISBN/EAN: 9781119053637
Sprache: englisch
Anzahl Seiten: 288

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Beschreibungen

<p><b>An in-depth introduction to the foundations of vibrations for students of mechanical engineering</b></p> <p>For students pursuing their education in Mechanical Engineering, <i>An Introduction to Mechanical Vibrations</i> is a definitive resource. The text extensively covers foundational knowledge in the field and uses it to lead up to and include: finite elements, the inerter, Discrete Fourier Transforms, flow-induced vibrations, and self-excited oscillations in rail vehicles.</p> <p>The text aims to accomplish two things in a single, introductory, semester-length, course in vibrations. The primary goal is to present the basics of vibrations in a manner that promotes understanding and interest while building a foundation of knowledge in the field. The secondary goal is to give students a good understanding of two topics that are ubiquitous in today's engineering workplace - finite element analysis (FEA) and Discrete Fourier Transforms (the DFT- most often seen in the form of the Fast Fourier Transform or FFT). FEA and FFT software tools are readily available to both students and practicing engineers and they need to be used with understanding and a degree of caution. While these two subjects fit nicely into vibrations, this book presents them in a way that emphasizes understanding of the underlying principles so that students are aware of both the power and the limitations of the methods.</p> <p>In addition to covering all the topics that make up an introductory knowledge of vibrations, the book includes:</p> <p>●          End of chapter exercises to help students review key topics and definitions</p> <p>●          Access to sample data files, software, and animations via a dedicated website</p>
<p>Preface xi</p> <p>About the Companion Website xv</p> <p><b>1 The Transition from Dynamics to Vibrations </b><b>1</b></p> <p>1.1 Bead on a Wire: The Nonlinear Equations of Motion 2</p> <p>1.1.1 Formal Vector Approach using Newton’s Laws 3</p> <p>1.1.2 Informal Vector Approach using Newton’s Laws 5</p> <p>1.1.3 Lagrange’s Equations of Motion 6</p> <p>1.1.3.1 The Bead on a Wire via Lagrange’s Equations 7</p> <p>1.1.3.2 Generalized Coordinates 9</p> <p>1.1.3.3 Generalized Forces 9</p> <p>1.1.3.4 Dampers – Rayleigh’s Dissipation Function 11</p> <p>1.2 Equilibrium Solutions 12</p> <p>1.2.1 Equilibrium of a Simple Pendulum 12</p> <p>1.2.2 Equilibrium of the Bead on the Wire 13</p> <p>1.3 Linearization 14</p> <p>1.3.1 Geometric Nonlinearities 14</p> <p>1.3.1.1 Linear EOM for a Simple Pendulum 15</p> <p>1.3.1.2 Linear EOM for the Bead on the Wire 17</p> <p>1.3.2 Nonlinear Structural Elements 18</p> <p>1.4 Summary 19</p> <p>Exercises 19</p> <p><b>2 Single Degree of Freedom Systems – Modeling </b><b>23</b></p> <p>2.1 Modeling Single Degree of Freedom Systems 23</p> <p>2.1.1 Deriving the Equation of Motion 24</p> <p>2.1.2 Equations of Motion Ignoring Preloads 27</p> <p>2.1.3 Finding Spring Deflections due to Body Rotations 29</p> <p>Exercises 34</p> <p><b>3 Single Degree of Freedom Systems – Free Vibrations </b><b>39</b></p> <p>3.1 Undamped Free Vibrations 39</p> <p>3.2 Response to Initial Conditions 41</p> <p>3.3 Damped Free Vibrations 44</p> <p>3.3.1 Standard Form for Second-Order Systems 46</p> <p>3.3.2 Undamped 47</p> <p>3.3.3 Underdamped 48</p> <p>3.3.4 Critically Damped 50</p> <p>3.3.5 Overdamped 51</p> <p>3.4 Root Locus 52</p> <p>Exercises 53</p> <p><b>4 SDOF Systems – Forced Vibrations – Response to Initial Conditions </b><b>59</b></p> <p>4.1 Time Response to a Harmonically Applied Force in Undamped Systems 59</p> <p>4.1.1 Beating 61</p> <p>4.1.2 Resonance 63</p> <p>Exercises 65</p> <p><b>5 SDOF Systems – Steady State Forced Vibrations </b><b>67</b></p> <p>5.1 Undamped Steady State Response to a Harmonically Applied Force 67</p> <p>5.2 Damped Steady State Response to a Harmonically Applied Force 70</p> <p>5.3 Response to Harmonic Base Motion 73</p> <p>5.4 Response to a Rotating Unbalance 77</p> <p>5.5 Accelerometers 82</p> <p>Exercises 85</p> <p><b>6 Damping </b><b>89</b></p> <p>6.1 Linear Viscous Damping 89</p> <p>6.2 Coulomb or Dry Friction Damping 93</p> <p>6.3 Logarithmic Decrement 96</p> <p>Exercises 97</p> <p><b>7 Systems with More than One Degree of Freedom </b><b>101</b></p> <p>7.1 2DOF Undamped Free Vibrations – Modeling 101</p> <p>7.2 2DOF Undamped Free Vibrations – Natural Frequencies 104</p> <p>7.3 2DOF Undamped Free Vibrations – Mode Shapes 106</p> <p>7.3.1 An Example 107</p> <p>7.4 Mode Shape Descriptions 110</p> <p>7.5 Response to Initial Conditions 112</p> <p>7.6 2DOF Undamped Forced Vibrations 115</p> <p>7.7 Vibration Absorbers 116</p> <p>7.8 The Method of Normal Modes 118</p> <p>7.9 The Cart and Pendulum Example 123</p> <p>7.9.1 Modeling the System – Two Ways 124</p> <p>7.9.1.1 Kinematics 124</p> <p>7.9.1.2 Newton’s Laws 125</p> <p>7.9.1.3 Lagrange’s Equation 127</p> <p>7.10 Normal Modes Example 129</p> <p>Exercises 132</p> <p><b>8 Continuous Systems </b><b>137</b></p> <p>8.1 The Equations of Motion for a Taut String 137</p> <p>8.2 Natural Frequencies and Mode Shapes for a Taut String 139</p> <p>8.3 Vibrations of Uniform Beams 142</p> <p>Exercises 151</p> <p><b>9 Finite Elements </b><b>153</b></p> <p>9.1 Shape Functions 153</p> <p>9.2 The Stiffness Matrix for an Elastic Rod 155</p> <p>9.3 The Mass Matrix for an Elastic Rod 161</p> <p>9.4 Using Multiple Elements 164</p> <p>9.5 The Two-noded Beam Element 167</p> <p>9.5.1 The Two-noded Beam Element – Stiffness Matrix 168</p> <p>9.5.2 The Two-noded Beam Element – Mass Matrix 171</p> <p>9.6 Two-noded Beam Element Vibrations Example 173</p> <p>Exercises 177</p> <p><b>10 The Inerter </b><b>181</b></p> <p>10.1 Modeling the Inerter 181</p> <p>10.2 The Inerter in the Equations of Motion 184</p> <p>10.3 An Examination of the Effect of an Inerter on System Response 186</p> <p>10.3.1 The Baseline Case – <i>p </i>= 0 187</p> <p>10.3.2 The Case Where the Inerter Adds Mass Equal to the Block’s Mass – <i>p </i>= 1 188</p> <p>10.3.3 The Case Where <i>p </i>is Very Large 188</p> <p>10.4 The Inerter as a Vibration Absorber 190</p> <p>Exercises 193</p> <p><b>11 Analysis of Experimental Data </b><b>195</b></p> <p>11.1 Typical Test Data 195</p> <p>11.2 Transforming to the Frequency Domain – The CFT 197</p> <p>11.3 Transforming to the Frequency Domain – The DFT 200</p> <p>11.4 Transforming to the Frequency Domain – A Faster DFT 202</p> <p>11.5 Transforming to the Frequency Domain – The FFT 203</p> <p>11.6 Transforming to the Frequency Domain – An Example 204</p> <p>11.7 Sampling and Aliasing 207</p> <p>11.8 Leakage and Windowing 212</p> <p>11.9 Decimating Data 216</p> <p>11.10 Averaging FFTs 225</p> <p>Exercises 228</p> <p><b>12 Topics in Vibrations </b><b>231</b></p> <p>12.1 What About the Mass of the Spring? 231</p> <p>12.2 Flow-induced Vibrations 233</p> <p>12.3 Self-Excited Oscillations of Railway Wheelsets 238</p> <p>12.4 What is a Rigid Body Mode? 249</p> <p>12.5 Why Static Deflection is Very Useful 251</p> <p>Exercises 254</p> <p><b>Appendix A: Least Squares Curve Fitting </b><b>257</b></p> <p><b>Appendix B: Moments of Inertia </b><b>261</b></p> <p>B.1 Parallel Axis Theorem for Moments of Inertia 262</p> <p>B.2 Moments of Inertia for Commonly Encountered Bodies 263</p> <p>Index 265</p>
<p><b>D<small>R</small>. RONALD J. ANDERSON</b> is a Professor in the Department of Mechanical and Materials Engineering, Queen's University at Kingston, Canada. He received his B.Sc.(Eng) from the University of Alberta in 1973, his M.Sc.(Eng) from Queen's University in 1974, and his Ph.D. from Queen's University in 1977. His doctoral research was in the field of road vehicle dynamics. From 1977 to 1979, he was a Defence Scientist with the Defence Research Establishment Atlantic where he was engaged in research on the dynamics of novel ships. From 1979 to 1981 he was Senior Dynamicist with the Urban Transportation Development Corporation where he worked on rail vehicle dynamics, particularly suspension design for steerable rail vehicles. He joined Queen's University in 1981 and, while conducting research into vehicle dynamics and multibody dynamics, has been teaching undergraduate courses on dynamics and vibrations and postgraduate courses on advanced dynamics and engineering analysis. Dr. Anderson has been the recipient of several departmental and faculty-wide teaching awards. He has also served the University in the academic administrative roles of Head of Department, Associate Dean (Research), and Dean of Graduate Studies.
<p><b>An in-depth introduction to the foundations of vibrations for students of mechanical engineering</b> <p>For students pursuing their education in Mechanical Engineering, <i>Introduction to Mechanical Vibrations</i> is a definitive resource. The text extensively covers foundational knowledge in the field and uses it to lead up to and include: finite elements, the inerter, Discrete Fourier Transforms, flow-induced vibrations, and self-excited oscillations in rail vehicles. <p>The text aims to accomplish two things in a single, introductory, semester-length, course in vibrations. The primary goal is to present the basics of vibrations in a manner that promotes understanding and interest while building a foundation of knowledge in the field. The secondary goal is to give students a good understanding of two topics that are ubiquitous in today's engineering workplace – finite element analysis (FEA) and Discrete Fourier Transforms (the DFT- most often seen in the form of the Fast Fourier Transform or FFT). FEA and FFT software tools are readily available to both students and practicing engineers and they need to be used with understanding and a degree of caution. While these two subjects fit nicely into vibrations, this book presents them in a way that emphasizes understanding of the underlying principles so that students are aware of both the power and the limitations of the methods. <p>In addition to covering all the topics that make up an introductory knowledge of vibrations, the book includes: <ul> <li>End of chapter exercises to help students review key topics and definitions</li> <li>Access to sample data files, software, and animations via a dedicated website</li> </ul>

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